The following table shows age distribution and location of a random sample of 166 buffalo in a national park.AgeLamar DistrictNez Perce DistrictFirehole DistrictRow TotalCalf16101541Yearling1091433Adult30243892Column Total564367166

Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: Age distribution and location are independent.

H₁: Age distribution and location are not independent.

H₀: Age distribution and location are independent.

H₁: Age distribution and location are independent.

H₀: Age distribution and location are not independent.

H₁: Age distribution and location are independent.

H₀: Age distribution and location are not independent.

H₁: Age distribution and location are not independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Yes

No

What sampling distribution will you use?

binomial

uniform

normal

chi-square

Student'st

What are the degrees of freedom?

(c) Find or estimate theP-value of the sample test statistic. (Round your answer to three decimal places.)

p-value > 0.100

0.050 <p-value < 0.100

0.025 <p-value < 0.050

0.010 <p-value < 0.025

0.005 <p-value < 0.010

p-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since theP-value >, we fail to reject the null hypothesis.

Since theP-value >, we reject the null hypothesis.

Since theP-value, we reject the null hypothesis.

Since theP-value, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that age distribution and location are not independent.

At the 5% level of significance, there is insufficient evidence to conclude that age distribution and location are not independent.